Muon spin spectroscopy has been used to study in detail the onset of large-moment antiferromagnetism (LMAF) in UPt_3 as induced by Th substitution. Zero-field experiments have been carried out on a series of polycrystalline U_1-xTh_xPt_3 (0 <= x <= 0.05) samples in the temperature range 0.04 - 10 K. At low Th content (x <= 0.002) magnetic ordering on the time scale of the uSR experiment (10^-8 s) is not detected. For x = 0.005 a weak magnetic signal appears below T = 2 K, while for 0.006 <= x

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... 0.05, spontaneous oscillations in the uSR spectra signal the presence of the LMAF phase. The data are well described by a two-component depolarization function, combining the contribution of a polycrystalline antiferromagnet and a Kubo-Lorentzian response. However, the transition into the antiferromagnetic phase is quite broad. For x = 0.01 and 0.02, a weak magnetic signal appears below about 7 K, which is well above the mean-field transition temperatures. The broadening may be a result of the effects of disorder on the time fluctuations associated with anomalous small-moment antiferromagnetism.